For example, for systems under the influence of a strong magnetic field, a partial alignment of the fermion spins leads to a population imbalance and a shift in the sizes of the Fermi surfaces. While in the BCS theory such a strong magnetic field would suppress superconductivity entirely [1]}, numerous proposals and extensions have arisen since then that might allow for such exotic pairing. For example, the minority spin species could pay the kinetic energy cost to promote fermions up to the Fermi level of the majority species, breaching the so-called Chandrasekhar-Clogston limit [2]}, [3]}, also referred to as the Pauli limit. Alternatively, pairing might form at the minority species Fermi level, leaving the fermions of the majority species above unpaired as in breached superconductivity [4]}, [5]}, [6]}. Yet another possibility was proposed by Fulde and Ferrell (FF) [7]}, and Larkin and Ovchinnikov (LO) [8]} where fermions remain at their respective Fermi levels and then pair from opposite sides, resulting in a Cooper pair with net momentum. The superconducting gap then oscillates at the concomitant wavevector with the FF phase having a single wavevector and the LO phase two equal but opposite wavevectors.
